Twins leaders are expected to speak in detail about the change during a Tuesday afternoon press conference.
Castellano had been with the major league club for 12 seasons. They will have a new manager for the 2019 season.
Several minor league coaches will not be brought back, including Class AAA Rochester hitting coach Chad Allen; Chattanooga pitching coach Ivan Arteaga; class A Cedar Rapids pitching coach Henry Bonilla; and Dominican Republic hitting coach Asdrubal Estrada.
A person familiar with the decision told USA TODAY Sports that the decision was made despite the fact Molitor was voted American League's Manager of the Year last season, and the fact he has two years left on his contract at a reported $3.25 million.
"I don't really think that that was a huge roadblock to them", Pohlad said.
"A lot of factors go into these decisions, every time, and Paul knows that", Falvey said. "So I feel good about that decision".
New version of NAFTA could be good for Ohio, experts say
Under the new agreement, three-quarters of a car's parts must originate from North America in order to be exempt from duties. Trump had described Nafta as a bad deal for Americans and threatened to eliminate it as part of his "America First" agenda.
"I will forever be grateful for the opportunity they gave me to serve in the role as manager for these past four years", Molitor continued in a release.
Offseason acquisitions such as designated hitter Logan Morrison, and starting pitchers Jake Odorizzi and Lance Lynn, were major disappointments, as well.
Falvey and other club executives expressed confidence that Molitor would stay with the Twins beyond the 20 years he has already worked for them in various roles, including the final three seasons of his Hall of Fame playing career.
"This is an eye toward the future", team president Dave St. Peter said. "We have to take some new steps moving forward".
"I also think there are number of managerial openings, and that it's going to be competitive for the top talent, and that's why we're prepared to start on immediately".